Less than 24 hours after the ink dried on Instagram’s latest financing round — an investment that valued it at roughly $500 million — Mr. Zuckerberg placed a call to Kevin Systrom, Instagram’s chief executive, according to people with knowledge of the matter, who spoke on the condition of anonymity because the discussions were private.

Mr. Zuckerberg was blunt: Facebook wanted to buy Instagram. Over the next 48 hours, Facebook and Instagram hammered out the details for a $1 billion cash-and-stock deal, the social network’s largest acquisition to date, the people said. By the end of Sunday, the deal was done and announced the following day.